Quote from: redwhite037 on March 27, 2014, 12:50:57 AM

I believe the current blockchain is around 15GB,

It is currently closer to 20 GB, and growing every 10 minutes.

Quote from: dolphin001 on March 27, 2014, 06:07:16 AM

1. Is there a way i could synchonize for only my transaction or at least transactions that happened close to my, including my?

Not with the Bitcoin Core wallet. If you didn't want to operate as a full node, you should have used one of the "light" wallet options such as:

MultiBit
Electrum
blockchain.info/wallet

Quote from: dolphin001 on March 27, 2014, 06:07:16 AM

I really don't see any reason why would I want to have saved entire history of everyone's btc usage.

Because Bitcoin Core is a full node on the bitcoin network. It verifies that every transaction and block properly follows the protocol, and relays those transactions and blocks to the other nodes on the network.

If you no longer want to operate as a full node, you can export the private key for your address from your wallet and import it into one of the "light" wallets listed above. blockchain.info even provides a method to create a wallet with their service by importing the entire wallet.dat file directly from Bitcoin Core.

Quote from: dolphin001 on March 27, 2014, 06:07:16 AM

2. Im planning to buy new computer soon and I would have to go through this procedure once again but is there any way to avoid it along known one - copy blocks files (from Application Data folder) from old to new computer?

Yes, if you copy the entire contents from the bitcoin data directory to the same directory on the new computer, then you can avoid needing to synchronize the entire blockchain again.

Quote from: dolphin001 on March 27, 2014, 06:07:16 AM

3. Once synchonizing is complete, can I permanently delete any of those blocks files from first time synchronizing?

No. If you do this, then Bitcoin Core will have to re-synchronize all the blocks again.